I found the solution from the second comment you provided, Trengot, thanks. It turns out that I had some dangling blobs, which were in
.git/objects/17 and hence triggering the packing:
$ git fsck dangling blob d9ff0aeac4aa8b4e0907daed675ebf60278bc977 dangling blob dbff2d073741f9775c815d4a3c623736af224dad dangling blob e1ffbab1c5b985cd1cd3bc0281075ea2ed80744a dangling blob fdff59878ccb3a75689f4acca615cfb635288774
This cleaned them up:
$ git gc --prune=now
Be aware, as per Henrik's comment below, this may be a little dangerous. Take care!